I checked my logs to count up the 54 bags of platinum I've bought over the past couple years on 3 accounts (which I started buying after running out of anything else to spend loyalty points on).
The platinum amount is random, the max range has been 13060 to 16879, but results were much more common within the 14000 - 16000 range, with the average amount very close to 15000.
If you're earning 120 loyalty points a week, that's good for one bag of 15k plat every month.